Journal of Petroleum Exploration and Production Technology (2019) 9:573–582
https://doi.org/10.1007/s13202-018-0501-0
ORIGINAL PAPER - PRODUCTION ENGINEERING
Estimating oil–gas ratio for volatile oil and gas condensate reservoirs:
artificial neural network, support vector machines and functional
network approach
Mohammed A. Khamis1 · K. A. Fattah1,2
Received: 29 October 2017 / Accepted: 4 June 2018 / Published online: 9 June 2018
© The Author(s) 2018
Abstract
Laboratory experiment ideally, is the main method to obtain PVT properties of the oil and gas reservoir fluids. The alternative two methods widely used when laboratory experiments are not available are: equation of state (EOS) and empirical PVT
correlations. The EOS requires lots of numerical computations based on identifying the full compositions of the reservoir
fluids properties. The measurement and calculation of these properties are very expensive and time consuming. On the other
hand, using of PVT correlations which are based on easily measured field data such as reservoir pressure and temperature,
and gas and oil density is reliable and more economic. In this work, three artificial intelligence (AI) technique models were
developed to predict the oil–gas ratio (Rv) for volatile oil and gas condensate reservoirs. Thirteen actual reservoir fluid
samples (five volatile oils and eight gas condensates) covering a wide range of fluid behavior and characteristics were used.
Whitson and Torp three parameters EOS were used to generate modified black oil (MBO) PVT properties that were used
as a data set for model development. The MBO PVT data points were extracted for each sample using commercial PVT
software at five different separator conditions. The nature of the input data was studied showing that data type is clustered.
In addition, the correlations between the input parameters were checked. This preprocessed is helpful in selecting the best
method to deal with the input parameters that will be fed to the developed models. According to this analysis and since the
input parameters have different ranges, normalization of these parameters is vital to improve the accuracy of the models
and to get the solution quickly and efficiently. Results showed that taking the log for the input parameters is the best among
the other normalization techniques. The AI techniques that have been implemented in this research are; Artificial Neural
Network (ANN) models, Functional Networks (FNs) and Support Vector Machines (SVMs). Models developed based on
these techniques used 17,941 data points and a ratio of 70% for training, 15% for validation, and 15% for testing. To develop
these models, three Matlab codes were written for each tool where the provided input data in excel format were read and
prepressed before implementation. Results obtained using these techniques showed that the ANN model predicted Rv with
an average square correlation coefficient of 0.9999 and an average relative error of 0.15% while FNs predicted Rv with an
average correlation coefficient of 0.9635 and an average relative error of 27.6%. It was noted that SVMs gave the best results
with an average correlation coefficient of 0.9990 and an average relative error of 0.12%. The results concluded that ANN
and SVM accurately predicted such data since this type of data are clustered and these two models can handle this kind of
data. The newly developed models depend only on easily obtainable parameters in the field and can have varied applications
when typical lab PVT reports are not available.
Keywords Oil–gas ratio model · PVT lab report · Gas condensate · Volatile oil · Modified black oil simulation · Artificial
neural network · Functional networks · Support vector machines
Introduction
* Mohammed A. Khamis
mokhamis@ksu.edu.sa
Extended author information available on the last page of the article
The conventional PVT properties for the reservoir fluids
black oil type are solution gas–oil ratio, Rs; oil formation
volume factor, Bo; and gas formation volume factor, Bg.
According to Fattah et al. (2009), the difference between
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the modified black oil (MBO) PVT properties and the conventional black oil PVT properties are in the handling of
the liquid in the gas phase, the oil–gas ratio, Rv. The MBO
approach supposes that the composition of stock tank liquid
can exist in both of the liquid and gas phases at reservoir
conditions. The liquid content of the gas phase was assumed
to be defined as a function of pressure named vaporized
oil–gas ratio, Rv. It is similar to the solution gas–oil ratio,
Rs, which is used to describe how much gas is dissolved in
the liquid phase. The MBO properties or extended black
oil was introduced for the first time by Spivak and Dixon
(1973).
Whitson and Torp (1983), formed a set of steps to estimate the MBO properties according to the constant volume
depletion (CVD) test data for the gas condensate. Coats,
1985, introduced a different method for gas condensate
reservoir using commercial software of EOS PVT and a
regression package to fit the PVT data obtained in the laboratory. McVay (1994), expanded Coats method for the volatile oil reservoir. Walsh and Towler (1994) also introduced
another method to compute the MBO properties from the
CVD experiment data of gas condensate. Fevang et al.
(2000), showed strategies to assist engineers in choosing
either MBO or compositional approaches. In 2006, Fattah
et al. presented a comparison between Whitson and Torp,
and Coats methods using compositional simulation. Results
show a good match between experimental PVT data and
the EOS model. Also in 2009, Fattah et al. developed a new
set of correlations to calculate the MBO properties of volatile oil and gas condensate. Alimadadi et al. (2011), predicted the PVT properties using ANN model. Component
mole fraction of the fluid sample, solution gas/oil ratio,
(Rs), bubble point pressure (Pb), reservoir pressure, API
oil gravity, and temperature were used as input parameters.
The model operated the input parameters using two parallel
multilayer perceptron (MLP) networks before the results
will be recombined.
Arief et al. (2017), proposed a technique of using surrogate models and the available laboratory database to estimate the fluid properties. Two surrogate models are studied
in his work: universal kriging and NN.
González et al. (2003) developed NN models to estimate
the dew point pressure for retrograde gas reservoirs. The
model accuracy was reported to be 8.74% in prediction.
Osman and Al-Marhoun (2005) established ANN models
to estimate several PVT properties; formation volume factor,
isothermal compressibility and brine density as a function
of temperature, salinity and pressure. Also they predict the
brine viscosity as a function of brine salinity and temperature. Developing these models was achieved using 1040 data
points.
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Oloso et al. (2009) predicted the crude oil viscosity and
gas–oil ratio using support vector machine and functional
network.
Ahmadi et al. (2015) utilized the NN technique to model
the bubble point pressure as a function of fluid composition
and other reservoir parameters. They used NN back propagation along with particle swarm optimization algorithm as an
optimization tool to minimize the error.
Sahterri et al. (2015) developed NN model to predict the
gas compressibility factor Z-factor using data set of 978
points. Their model estimated the Z-factor with 2.3% average relative error using Wilcoxon generalized radial basis
function network.
Adeeyo (2016) developed NN models to predict the bubble point pressure and formation volume factor at bubble
point pressure for Nigerian crude oils. Trial and error technique was used to come up with the best number of neurons
that gave stable results.
Artificial intelligent technique models
Artificial neural network
An artificial neural network (ANN) defined as data processing model analogous to biological nervous systems,
such as the brain and data processing. The most important
component of this model is the innovative structure system
of processing the information. It consists of a big number
of extremely consistent elements or neurons which are in a
harmony work to solve definite problems. ANNs, can learn
by example like people. The ANN can be constructed for a
definite application, such as pattern recognition or classification of data, over a process of learning. This process in
biological systems includes modifications to the synaptic
connections which exist between the imaginary neurons.
For the last two decades, AI has been sued extensively
in several applications in oil industry. A good number
of studies have been done using various computational
intelligence (CI) schemes to forecast the characteristics
of gas and oil flow through reservoirs and pipes using
such schemes including logistic regression (LR) (Hosmer and Lemeshow 2000), multilayer perceptrons (MLP)
(Wlodzisław et. al. 1997), and radial basis function (RBF)
(Guojie 2004).
Functional networks
Functional networks (FNs) are modification of neural networks which consist of many layers of neurons that are
connected through links. A simple calculation is performed
in each computing unit or neuron. A special scalar function
Journal of Petroleum Exploration and Production Technology (2019) 9:573–582
f of a weighted sum of inputs is linked with the neurons and
with the use of well-known algorithms learning from the
used data is processed. The functional networks main idea
involves the allowance of learning the f functions during
suppressing the weights. In addition, these functions of
multidimensional can be consistently substituted by single
variables functions. With the multiple n links that move
from the last layer of neurons into an output unit which
can will be written through a number of different forms
for each different link. This procedure will generate a system of n − 1 equations. This system can be written directly
from the neural network topology. Solving such system of
equations will simplify the initial functions f linked with
the neurons. Castillo et al. (2001) provided an inclusive
demonstration showing the application of FN in the field
of engineering and statistics. It was, however, observed
in the literature that not much has been applied in of oil
industry field.
Support vector machines
Support vector machines (SVMs) are a group of connected
supervised learning methods that have been applied for
organization and regression as well. These set of methods
follow a group of generalized linear classifiers. They can
also be treated as a special case of Tikhonov regularization. SVMs correlate the input vectors to a higher dimensional space where a maximal braking hyperplane is made.
Two parallel hyperplanes are produced on each side of the
hyperplane that splits the data. During this process a certain
575
assumption is assumed that the greater the distance between
these parallel hyperplanes, the better the abstraction error of
the classifier will be (Burges 1998).
SVMs have been used widely in many engineering fields
including defect prediction in software engineering (Elish
and Elish 2007), surface tension prediction in chemistry (Jie
Wang et. al. 2007), geotechnical engineering (Anthony and
Goh 2007) and oil and gas (Jian and Wenfen 2006) with very
promising results.
Fluid samples used
Fattah (2005) exposed PVT experiment data for thirteen reservoir fluid samples [eight gas condensates, (GC), and five
volatile oils, (VO)]. The result of these PVT experiments
data was used in this study. The samples were gotten from
reservoirs demonstrating different locations and depth, and
were selected to cover a wide range of oil and gas fluid characteristics. Some samples characterize near critical fluids
(VO 2, VO 5, GC 1, and GC 2) as clarified by McCain and
Bridges (1994). Table 1 presents a description of the major
properties of these thirteen fluid samples.
EOS approach
For every sample in Table 1, an EOS model that matches the
experimental results of all available PVT laboratory experiments (CCE, DL, CVD, and separator tests) was derived.
Table 1 Characteristics of fluid samples (Fattah et al. 2009)
Property
VO 1 VO 2 VO 3 VO 4 VO 5
GC 1
GC 2 GC 3 GC 4 GC 5 GC 6
GC 7 GC 8
Reservoir temperature (°F)
Initial reservoir pressure (psig)
Initial producing gas–oil ratio (SCF/STB)
Stock oil gravity (°API)
Saturation pressure (psig)
249
NA
1991
45.5
4527
312
14,216
3413
45.6
5210
286
NA
4278
NA
5410
300
5985
6500
45.6
5800
Components
Composition (mole%)
CO2
N2
C1
C2
C3
iC4
nC4
iC5
nC5
C6
C7+
2.14 2.18 2.4
0.1
0.34
0.11 1.67 0.31 0.16 0
55.59 60.51 56.94 69.84 72.47
8.7
7.52 9.21 5.37 4.57
5.89 4.74 5.84 3.22 2.79
1.36 4.12 1.44 0.87 0.67
2.69 0
2.73 1.7
1.33
1.17 2.97 1.03 0.79 0.69
1.36 0
1.22 0.88 0.82
1.97 1.38 1.96 1.41 1.52
19.02 14.91 16.92 15.66 14.8
2.66
0.17
59.96
7.72
6.50
1.93
3.00
1.64
1.35
2.38
12.69
4.48 0.14 0.01 0.18 2.79
0.70 1.62 0.11 0.13 0.14
66.24 63.06 68.93 61.72 66.73
7.21 11.35 8.63 14.1 10.22
4.00 6.01 5.34 8.37 5.90
0.84 1.37 1.15 0.98 1.88
1.76 1.94 2.33 3.45 2.10
0.74 0.84 0.93 0.91 1.37
0.87 0.97 0.85 1.52 0.83
0.96 1.02 1.73 1.79 1.56
12.2 11.68 9.99 6.85 6.48
246
5055
2000
51.2
4821
260
5270
2032
NA
4987
190
NA
2424
36.8
7437
197
13,668
2416
34.1
9074
238
6000
NA
NA
4815
256
7000
4697
46.5
6010
186
5728
5987
58.5
4000
312
14,216
8280
50.7
5465
233
17,335
6665
43
11,475
6.98 0.36
1.07 0.31
65.25 81.23
8.92 5.54
4.81 2.66
0.85 0.62
1.75 1.06
0.65 0.47
0.69 0.52
0.83 0.84
8.2
6.39
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For consistency, all EOS models were developed using
Peng and Robinson (1976) EOS with volume shift correction (three-parameter EOS) (Fattah 2005). The procedure
suggested by Coats and Smart (1986) to match the laboratory results was followed. Then the developed EOS model
for each sample was used to obtain MBO PVT properties
at different separator conditions using Whitson and Torp
(1983) procedure. The MBO PVT properties include the four
functions required for MBO simulation are (Rv, Rs, Bo, and
Bg). Our database of Rv data consists of 1850 points from
eight different gas condensate samples and 1180 points from
five volatile oil samples. PVTi module of Eclipse was used
to generate our database of Rv data.
Table 2 Input data statistics
Minimum
Maximum
Range
Three Matlab codes were written for each tool to develop
these AI models where the provided input data in excel format was read and prepressed before implementation. The
ANN model and the other models were developed using 13
actual reservoir fluid samples. Table 2 represents statistical
analysis of the input data. The data used as input for the
three models developed in this study include reservoir pressure in psi, reservoir temperature in °R, reservoir bubble
point pressure in psi, oil density and gas density at stock
tank conditions in lb/cu, condensate yield, bbl/MMscf, and
Ps (Psia)
Temp (F)
Pb (Psia)
ρo (lb/scf)
ρg (lb/scf)
Condensate
yield (STB/
scf)
Rv (STB/scf)
714.7
9523.9
8809.2
650
772
122
2666.7
11490.0
8823.3
47.45
53.46
6.01
0.0514
0.0789
0.0275
24.53
458.80
434.27
0.3175
458.8
458.5
Fig. 1 Feedforward backpropagation, Type 1
Fig. 2 Trainable cascade-forward backpropagation, Type 2
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Rv models using artificial intelligence
techniques
Journal of Petroleum Exploration and Production Technology (2019) 9:573–582
oil–gas ratio Rv, while the output parameter is the oil–gas
ratio Rv.
Results and discussion
The ANN model architecture in terms of number of neurons, layers and the type of connection function were determined based on trial and error process because it was the
most successful criteria in developing the model. Two neural network types were used; feedforward backpropagation
Table 3 Neural network results
Neural network type
Feedforward backpropagation
Trainable cascade-forward
backpropagation
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(Type 1, Fig. 1) and trainable cascade-forward backpropagation (Type 2, Fig. 2). On the other hand, different transfer
functions were tested and it was found that the best function was log sigmoid. However, the best neural network or
learning algorithm for training was of Type 2. Several problems were faced during training the network. The model
was trapped at some point and caused the training to be
sopped. This problem was related to the local minimum. To
overcome this problem, the maximum number of validation
failure was increased to 300 to get the global minimum. To
Number
of layers
Number of neurons
2
3
4
2
3
4
4–8
4–8–4
4–8–4–2
4–8
4–8–4
4–8–4–2
Correlation coefficient
Training
Validation
Testing
All
0.9983
0.9995
0.9997
0.9982
0.9999
1.0
0.9984
0.9995
0.9997
0.9980
0.9999
1.0
0.9983
0.9995
0.9997
0.9975
0.9999
1.0
0.9983
0.9995
0.9997
0.9980
0.9999
1.0
Table 4 Statistical comparison of all models and correlations
Absolute error %
Minimum
Maximum
Average
NN
FN
SVM
Rv correlation
Trained data
Super testing
Trained data
Super testing
Trained data
Super testing
0.0000
6.1150
0.1496
0.0001
3.9380
0.3125
0.0304
211.9021
27.6428
0.0584
222.7995
27.3328
0.000168
0.258926
0.122188
0.000334
0.790490
0.121292
0.055846
79.637
19.04
Fig. 3 Results of type-1 neural
network using two hidden layers
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train the network, 70% of the data was used while 15% was
used for validation and the other 15% for testing.
Table 3 shows a summary of the results indicating that
neural network of Type 2 gives better prediction using three
hidden layers. Of course using more hidden layers will
increase the accuracy of the results but it is time consuming.
Table 4 exhibits the statistics of the Rv correlation (Fattah
2005) as compared with the new neural network models generated. From this table, one can easily recognize that the new
models from the NN and SVM are the best matching models which give the lowest average absolute error 0.1496 and
Fig. 4 Results of type-1 neural
network using three hidden
layers
Fig. 5 Results of type-2 neural
network using two hidden layers
13
0.1222%, respectively. To validate the developed models, super
testing was done based on unseen data. According to this test,
SVM is the best method in terms of accurate prediction with
an average relative error of 0.121% followed by NN model
with an average relative error of 0.313. On the other hand, FN
was the worst model with an average relative error of 27.3%.
Figures 3 and 4 present the graphical representation of the
results of Type 1 neural network using two and three layers,
respectively. On the other hand, Figs. 5 and 6 display the
results of neural network of Type 2.
Journal of Petroleum Exploration and Production Technology (2019) 9:573–582
579
Fig. 6 Results of type-2 neural
network using three hidden
layers
Functional Networks were applied using 70% of the
data for training and 30% for testing. Since the range of
the input parameters is different as shown in Table 2, the
logarithmic values of the input parameters was taken as a
normalization method to improve the accuracy of the FN
technique. This tool gives results of correlation coefficient
of 0.965 for training and 0.962. Figure 7 represents the correlation between the predicted and the actual Rv for training which shows good match while Fig. 8 was for testing.
Similarly, Fig. 9 displays the cross-plot of the predicted
versus the actual Rv for training, whereas Fig. 10 displays
the cross-plot for testing. The results show good agreement
but it is not as good as the results obtained using the ANN
for both the training and testing although FN is a type of
ANN but it is not good in prediction for clustered data as
the ANN do.
SVMs with different kernel functions (Poly, Gaussian, polyhomog, htrbf, and rbf) were used. SVMs were
applied using 70% of the data for training and 30% for
testing. It was noted that for this type of data only Poly
and Gaussian kernel functions were working. This technique gives results of correlation coefficient of 0.995 for
training and 0.999 for testing. Figure 11 represents the
Result of Training for Oil Gas Ratio using FN
600
Predicted
Actual
Result of Testing for Oil Gas Ratio using FN
600
Predicted
Actual
500
500
400
Oil Gas Ratio
Oil Gas Ratio
400
300
200
200
100
0
300
100
0
200
400
600
800
1000
Data Points
1200
1400
1600
1800
Fig. 7 Predicted and actual Rv as a function of data points using FN
for training
0
0
100
200
300
400
Data Points
500
600
700
800
Fig. 8 Predicted and the actual Rv as a function of data points using
FN for testing
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Result of Training for Oil Gas Ratio using FN
600
Result of Testing for Oil Gas Ratio using SVM
500
Predicted
Actual
450
400
350
400
Oil Gas Ratio
Oil Gas Ratio - Measured
500
300
200
300
250
200
150
100
100
50
0
0
100
200
300
400
500
Oil Gas Ratio - Calculated
0
600
100
200
300
400
Data Points
500
600
700
800
Fig. 12 Predicted and the actual Rv as a function of data points using
SVM for testing
Fig. 9 Cross-plot of Rv using FN for training
Result of Testing for Oil Gas Ratio using FN
600
0
Result of Testing for Oil Gas Ratio using SVM
500
450
Oil Gas Ratio - Measured
Oil Gas Ratio - Measured
500
400
300
200
400
350
300
250
200
150
100
50
100
0
0
0
100
200
300
400
500
0
50
100
600
150
200
250
300
350
Oil Gas Ratio - Calculated
400
450
500
450
500
Oil Gas Ratio - Calculated
Fig. 13 Cross-plot of Rv using SVM for training
Fig. 10 Cross-plot of Rv using FN for testing
Result of Testing for Oil Gas Ratio using SVM
500
Result of Training for Oil Gas Ratio using SVM
500
450
450
Oil Gas Ratio - Measured
Predicted
Actual
400
Oil Gas Ratio
350
300
250
200
150
400
350
300
250
200
150
100
100
50
50
0
0
0
200
400
600
800
1000
Data Points
1200
1400
1600
1800
Fig. 11 Predicted and actual Rv as a function of data points using
SVM for training
13
0
50
100
150
200
250
300
350
Oil Gas Ratio - Calculated
Fig. 14 Cross-plot of Rv using SVM for testing
400
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Fig. 15 Error comparison
between neural network and
support vector machine models
581
10
Neural Network model
9
Support Vector Machine model
Relave Absolute Error %
8
7
6
5
4
3
2
1
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Pressure, psi
correlation between the predicted and the actual Rv for
training which shows good match while Fig. 12 was for
testing. Similarly, Fig. 13 displays the cross-plot of the
predicted versus the actual Rv for training whereas Fig. 14
displays the cross-plot for testing. The results show better prediction compared with FN but it is not as good as
the results obtained using the ANN for both the training
and testing. The advantage of the SVM compare with the
ANN is the run time is less. For this type of data only
Poly and Gaussian kernel functions were working.
Figure 15 represents additional comparison between
NN and SVM models in terms of average relative error
percent against pressure range. It was shown that SVM is
much better than NN.
Conclusions
• The Artificial Neural Network, Support Vector Machine
•
•
•
•
and Functional network techniques are effectively useful to estimate the oil–gas ratio.
The input and output parameters were preprocessed and
the log normalization method is implemented which
give better results for FN and SVM techniques.
Support Vector Machines give better results than Functional Networks with an average correlation coefficient
of 0.9970 and 0.9935, respectively.
Since the analysis of the data indicated that the nature
of the data is clustered for most of the input and output
parameters, the ANN and SVM give the best results with
an average relative error of 0.15 and 0.12%, correspondingly because these models are more flexible to deal with
such data.
Super testing results also confirm the research conclusions.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat​iveco​
mmons​.org/licen​ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate
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Affiliations
Mohammed A. Khamis1 · K. A. Fattah1,2
K. A. Fattah
kelshreef@ksu.edu.sa
1
Petroleum and Natural Gas Engineering Department,
College of Engineering, King Saud University, P.O.
Box 800, Riyadh 11421, Saudi Arabia
13
2
Petroleum Engineering Department, Faculty of Engineering,
Cairo University, Cairo, Egypt